Abstract. The canonical decomposition of higher-order tensors is a key tool in multilinear algebra. First we review the state of the art. Then we show that, under certain conditions, the problem can be rephrased as the simultaneous diagonalization, by equivalence or congruence, of a set of matrices. Necessary and sufficient conditions for the uniqueness of these simultaneous matrix decompositions are derived. In a next step, the problem can be translated into a simultaneous generalized Schur decomposition, with orthogonal unknowns [A.-J. van der Veen and A. Paulraj, IEEE Trans. Signal Process., 44 (1996), pp. 1136–1155]. A first-order perturbation analysis of the simultaneous generalized Schur decomposition is carried out. We discuss some computational techniques (including a new Jacobi algorithm) and illustrate their behavior by means of a number of numerical experiments.

A three-dimensional (3D) tongue model has been developed using MR images of a reference subject producing 44 artificially sustained Swedish articulations. Based on the difference in tongue shape between the articulations and a reference, the six linear parameters jaw height, tongue body, tongue dorsum, tongue tip, tongue advance and tongue width were determined using an ordered linear factor analysis controlled by articulatory measures. The first five factors explained 88 % of the tongue data variance in the midsagittal plane and 78 % in the 3D analysis. The six-parameter model is able to reconstruct the modelled articulations with an overall mean reconstruction error of 0.13 cm, and it specifically handles lateral differences and asymmetries in tongue shape. In order to correct articulations that were hyperarticulated due to the artificial sustaining in the magnetic resonance imaging (MRI) acquisition, the parameter values in the tongue model were readjusted based on a comparison of virtual and natural linguopalatal contact patterns, collected with electropalatography (EPG). Electromagnetic articulography (EMA) data was collected to control the kinematics of the tongue model for vowel-fricative sequences and an algorithm to handle surface contacts has been implemented, preventing the tongue from protruding through the palate and teeth. Ó 2002 Elsevier B.V. All rights reserved. Resume

. This paper approaches the articulatory-to-acoustic speech production inverse case. A framework based on an explicit combination of vocal-tract morphological and acoustic constraints is proposed. The solution is based on a Fourier analysis of the vocal-tract log-area function: the relationship between the log-area Fourier cosine coefficients and the corresponding formants is used to formulate an acoustic constraint. The same set of coefficients is then used to express a morphological constraint. This representation of both acoustic and morphological constraints in the same parameter space allows an efficient solution for the inverse problem. The basis of the acoustic constraint formulation was first proposed by Mermelstein (1967). However, at that time, the combination with morphological constraints was not realized. The method is tested for some vowels. The results confirm the validity of the method, but they also show the need for dynamic constraints. Zusammenfassung. Diese Arbeit...

Statistical articulatory modeling is based on the analysis of a collected speech corpus to extract parameters that should be able to resynthesize the articulatory movements in the original corpus.

This study examines the movement trajectories of the dorsal tongue movements during symmetrical /VCa /-sequences, where /V / was one of the Hungarian long or short vowels /i,a,u / and C either the voiceless palatal or velar stop consonants. General aims of this study were to deliver a data-driven account for (a) the evidence of the division between dorsality and coronality and (b) for the potential role coarticulatory factors could play for the relative frequency of velar palatalization processes in genetically unrelated languages. Results suggest a clear-cut demarcation between the behaviour of purely dorsal velars and the coronal palatals. Morevover, factors arising from a general movement economy might contribute to the palatalization processes mentioned. 1

Segmenting the acoustic signal in the TIMIT database by a switching state Kalman filter model is reported in this paper. According to the assumption that the high dimensional acoustic feature vector of the LSF (Line Spectrum Frequency) of the speech signal is probably embedded in a low dimensional space, a two dimensional vector is used to represent the continuous state vector in this model. The parameters of the model are initialized by PPCA (probabilistic principle component analysis) and first order vector auto-regression, and are re-estimated by the EM algorithm. We show that this model can be used to classify vowels, nasals, frication and silence by an approximate Viterbi inference. 1.

this paper is to demonstrate that PARAFAC successfully represents the three-dimensional shape of the tongue surface extracted from coronal magnetic resonance (MR) image stacks. Two types of measurement vectors are analyzed: a vector of 3D pseudo-fleshpoint coordinates extracted uniformly from the length and width of the tongue surface, and a vector of 2D pseudo-fleshpoint coordinates extracted from a curve along the tongue surface close to the midsagittal plane. The 2D pseudo-fleshpoint coordinates are structurally similar to the type of data analyzed by Nix et al. (1996). Measurement data are indexed by speaker identity, phonemic vowel identity, and twodimensional measurement position. A variety of data pre-processing strategies were attempted; the method that yields the best results is similar but not identical to the preprocessing methods of Nix et al. (1996)

This paper uses principal components (PC) analysis to represent coronal tongue contours for the eleven vowels of English in two consonant contexts (/s/, /l/), based upon five replicated measurements in three sessions for each of six subjects. Curves from multiple sessions and speakers were overlaid before analysis onto a common (x, y) coordinate system by extensive preprocessing of the curves including: extension (padding) or truncation within session, translation, and truncation to a common x-range. Four PC's plus a mean level allow accurate representation of coronal tongue curves, but PC shapes depend strongly on the degree of padding or truncation. The PC's successfully reduced the dimensionality of the curves and reflected vowel height, consonant context, and physiological features.

c○Leo Jingyu Lee 2004I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research.

Abstract. It is known that a high order tensor does not necessarily have an optimal low rank approximation, and that a tensor might not be orthogonally decomposable (i.e., admit a tensor SVD). We provide several sufficient conditions which lead to the failure of the tensor SVD, and characterize the existence of the tensor SVD with respect to the Higher Order SVD (HOSVD) of a tensor. In face of these difficulties to generalize standard results known in the matrix case to tensors, we consider low rank orthogonal approximations of tensors. The existence of an optimal approximation is theoretically guaranteed under certain conditions, and this optimal approximation yields a tensor decomposition where the diagonal of the core is maximized. We present an algorithm to compute this approximation and analyze its convergence behavior. Key words. multilinear algebra, singular value decomposition, tensor decomposition, low rank approximation AMS subject classifications. 15A69, 15A18